Lab- Simple Harmonic Motion
Objective: To find the spring constant of a spring in two ways (static and dynamic).
Analysis-
1. For your data from Part 1 above, plot the applied force F = gm vs the resulting displacement of the end of the spring (x - xo). Which quantity is the independent variable and which the dependent variable? This relationship should be linear. Construct a best-fit line, determine the slope, and calculate a value for the spring constant, k.
2. Using your data from Part 2 above, plot a graph of the period squared P2 (on the y-axis) vs the mass (on the x-axis). This curve should be close to being a linear relationship; determine the constants for a linear fit to these data. One of the constants will yield k, the spring constant. Compare this value of k to that found in step 1 and compute the percent difference (difference between the values divided by the average, times 100%).
3. Although the relationship you obtained in Part 2 may look linear, there was an omission in the theory. How much mass is actually oscillating during your experiments? The simplest theoretical correction is to add one third of the extra mass to the value of the oscillating mass. Replot your data using this correction. How does the correction affect your comparison of the values of k?